Turbine bucket having part-span connector and profile

ABSTRACT

Various embodiments of the invention include turbine buckets and systems employing such buckets. Various particular embodiments include a turbine bucket having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; a pair of part-span connectors extending from the airfoil at the suction side and the pressure side, respectively, wherein each of the pair of part-span connectors is located between approximately 40 percent and approximately 70 percent of a radial span measured from the base to a radial tip of the airfoil; and a base connected with a first end of the airfoil along the suction side, pressure side, trailing edge and the leading edge.

FIELD OF THE INVENTION

The subject matter disclosed herein relates to turbomachines. More particularly, the subject matter disclosed herein relates to components within turbomachines such as gas and/or steam turbines.

BACKGROUND OF THE INVENTION

Some aircraft and/or power plant systems, for example certain jet aircraft, nuclear, simple cycle and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. Some of these turbines employ airfoils (e.g., turbine blades, blades, airfoils, etc.) which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of these airfoils have an impact on system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION OF THE INVENTION

Various embodiments of the invention include turbine buckets and systems employing such buckets. Various particular embodiments include a turbine bucket having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and a base connected with a first end of the airfoil along the suction side, pressure side, trailing edge and the leading edge, the base including a part-span connector proximate a junction between the base and the airfoil.

A first aspect of the invention includes a turbine bucket having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; a pair of part-span connectors extending from the airfoil at the suction side and the pressure side, respectively, wherein each of the pair of part-span connectors is located between approximately 40 percent and approximately 70 percent of a radial span measured from the base to a radial tip of the airfoil; and a base connected with a first end of the airfoil along the suction side, pressure side, trailing edge and the leading edge.

A second aspect of the invention includes a turbine rotor section including: a set of buckets, the set of buckets including at least one bucket having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; a pair of part-span connectors extending from the airfoil at the suction side and the pressure side, respectively, wherein each of the pair of part-span connectors is located between approximately 40 percent and approximately 70 percent of a radial span measured from the base to a radial tip of the airfoil; and a base connected with a first end of the airfoil along the suction side, pressure side, trailing edge and the leading edge, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Z coordinate values are non-dimensional values of from 0 to 1 convertible to Z distances by multiplying the Z values by an airfoil height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, the X, Y, and Z distances being scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.

A third aspect of the invention includes a turbine bucket having: a static nozzle section; and a rotor section at least partially contained within the static nozzle section, the rotor section having a set of static buckets including at least one bucket having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and a base connected with a first end of the airfoil along the suction side, pressure side, trailing edge and the leading edge, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the coordinate values are non-dimensional values of from 0 to 1 convertible to Z distances by multiplying the Z values by an airfoil height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, the X, Y, and Z distances being scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of this invention will be more readily understood from the following detailed description of the various aspects of the invention taken in conjunction with the accompanying drawings that depict various embodiments of the invention, in which:

FIG. 1 shows a three-dimensional partial cut-away perspective view of a portion of a turbine according to an embodiment of the invention.

FIG. 2 shows a schematic three-dimensional depiction of a turbine bucket including an airfoil and a base, from a first angle, according to various embodiments of the invention.

FIG. 3 shows a schematic three-dimensional depiction of the turbine bucket of FIG. 2, from a second angle, according to various embodiments of the invention.

FIG. 4 shows a schematic three-dimensional depiction of a set of two adjacent turbine buckets according to various embodiments of the invention.

FIG. 5 shows a schematic three-dimensional depiction of a plurality of turbine buckets according to various embodiments of the invention.

FIG. 6 shows a schematic block diagram illustrating portions of a multi-shaft combined cycle power plant system according to embodiments of the invention; and

FIG. 7 shows a schematic block diagram illustrating portions of a single-shaft combined cycle power plant system according to embodiments of the invention.

It is noted that the drawings of the invention are not necessarily to scale. The drawings are intended to depict only typical aspects of the invention, and therefore should not be considered as limiting the scope of the invention. It is understood that elements similarly numbered between the FIGURES may be substantially similar as described with reference to one another. Further, in embodiments shown and described with reference to FIGS. 1-6, like numbering may represent like elements. Redundant explanation of these elements has been omitted for clarity. Finally, it is understood that the components of FIGS. 1-6 and their accompanying descriptions may be applied to any embodiment described herein.

DETAILED DESCRIPTION OF THE INVENTION

As noted herein, various aspects of the invention are directed toward turbine buckets. Particular aspects of the invention include turbine buckets having a base with a part-span connector.

In contrast to conventional turbine buckets, aspects of the invention include a turbine bucket (e.g., a dynamic bucket for driving a turbine shaft) having a pair of part-span connectors extending from the airfoil at the suction side and the pressure side, respectively. In some cases, each of the pair of part-span connectors is located between approximately 40 percent and approximately 70 percent of a radial span measured from the base to a radial tip of the airfoil. This part-span connector can provide for enhanced performance, efficiency and/or durability of the bucket (and associated turbine stages and turbine machines) when compared with conventional buckets.

As used herein, the terms “axial” and/or “axially” refer to the relative position/direction of objects along axis A, which is substantially parallel to the axis of rotation of the turbomachine (in particular, the rotor section). As further used herein, the terms “radial” and/or “radially” refer to the relative position/direction of objects along axis (r), which is substantially perpendicular with axis A and intersects axis A at only one location. Additionally, the terms “circumferential” and/or “circumferentially” refer to the relative position/direction of objects along a circumference which surrounds axis A but does not intersect the axis A at any location. Further, the term leading edge refers to components and/or surfaces which are oriented upstream relative to the fluid flow of the system, and the term trailing edge refers to components and/or surfaces which are oriented downstream relative to the fluid flow of the system.

In the following description, reference is made to the accompanying drawings that form a part thereof, and in which is shown by way of illustration specific embodiments in which the present teachings may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the present teachings and it is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the present teachings. The following description is, therefore, merely exemplary.

Referring to the drawings, FIG. 1 shows a perspective partial cut-away illustration of a turbine 10 (e.g., a gas or steam turbine) according to various embodiments of the invention. Turbine 10 includes a rotor 12 that includes a rotating shaft 14 and a plurality of axially spaced rotor wheels 18. A plurality of rotating buckets 20 (dynamic buckets) are mechanically coupled to each rotor wheel 18. More specifically, buckets 20 are arranged in rows that extend circumferentially around each rotor wheel 18. A static nozzle section 21 is shown including a plurality of stationary nozzles 22 that circumferentially around shaft 14, and the nozzles 22 are axially positioned between adjacent rows of buckets 20. Stationary nozzles 22 cooperate with buckets 20 to form a stage of the turbine 10, and to define a portion of a flow path through turbine 10. As shown, the static nozzle section 21 at least partially surrounds the rotor 12 (shown in this cut-away view). It is understood that the turbine 10 shown is a dual-flow turbine 10 that includes an axially centered inlet mouth which feeds two sets of turbine stages. It is understood that various teachings can be applied to axial turbines, e.g., axial inlet gas turbines that inlet a combustion gas from a first axial end and outlet that combustion gas to a second axial end after the gas has performed mechanical work on the turbine.

Returning to FIG. 1, in operation, gas 24 enters an inlet 26 of turbine 10 and is channeled through stationary nozzles 22. Nozzles 22 direct gas 24 against blades 20. Gas 24 passes through the remaining stages imparting a force on buckets 20 causing shaft 14 to rotate. At least one end of turbine 10 may extend axially away from rotating shaft 12 and may be attached to a load or machinery (not shown) such as, but not limited to, a generator, and/or another turbine.

In one embodiment, turbine 10 may include five stages. The five stages are referred to as L0, L1, L2, L3 and L4. Stage L4 is the first stage and is the smallest (in a radial direction) of the five stages. Stage L3 is the second stage and is the next stage in an axial direction. Stage L2 is the third stage and is shown in the middle of the five stages. Stage L1 is the fourth and next-to-last stage. Stage L0 is the last stage and is the largest (in a radial direction). It is to be understood that five stages are shown as one example only, and each turbine may have more or less than five stages. Also, as will be described herein, the teachings of the invention do not require a multiple stage turbine. In another embodiment, turbine 10 may comprise an aircraft engine used to produce thrust.

Turning to FIGS. 2 and 3, schematic three-dimensional depictions of a turbine bucket (or simply, bucket) 200 are shown, from distinct angles, according to various embodiments. The bucket 200 is a rotatable (dynamic) bucket which is part of a set of buckets circumferentially dispersed about a rotor shaft in a stage of a turbine (e.g., turbine 10). That is, during operation of a turbine (e.g., turbine 10), the bucket 200 will rotate about the axis A as a working fluid (e.g., gas or steam) is directed across the bucket's airfoil, initiating rotation of a rotor shaft (e.g., shaft 14). It is understood that bucket 200 is configured to couple (mechanically couple via fasteners, welds, slot/grooves, etc.) with a plurality of similar or distinct buckets (e.g., buckets 200 or other buckets) to form a set of buckets in a stage of the turbine.

The turbine bucket 200 can include an airfoil 202 having a suction side 204 (FIG. 3), and a pressure side 206 opposing the suction side 204. The bucket 200 can also include a leading edge 208 spanning between the pressure side 206 and the suction side 204, and a trailing edge 210 opposing the leading edge 208 and spanning between the pressure side 206 and the suction side 204.

As shown, the bucket 200 can also include a base 212 connected with the airfoil 202. The base 212 can be connected with the airfoil 202 along the suction side 204, pressure side 206, trailing edge 210 and the leading edge 208. In various embodiments, the bucket 200 includes a fillet 214 proximate a first end 215 of the airfoil 202, the fillet 214 connecting the airfoil 202 and the base 212. The fillet 214 can include a weld or braze fillet, which may be formed via conventional MIG welding, TIG welding, brazing, etc. As is known in the art, the base 212 is designed to fit into a mating slot in the turbine rotor shaft (e.g., shaft 14) and mate with adjacent base components of other buckets 200. The base 212 is designed to be located radially inboard of the airfoil 202. Bucket 200 can also include a shroud 216 radially outboard of airfoil 202, and connected with airfoil 202 via a fillet or other conventional weld.

As described herein, and in contrast to conventional turbine buckets, the turbine bucket 200 can include an airfoil 202 with a pair of part-span connectors 218 extending from airfoil 202 at suction side 204 and pressure side 206, respectively. Each of the pair of part-span connectors 218 is located between approximately 40 percent and approximately 70 percent of a radial span (R_(s)) measured from the base 212 to a radial tip 217 of airfoil 202 (at junction of shroud 216 and airfoil 202). In some embodiments each part-span connector 218 is located between approximately 56 percent and 58 percent of the radial span (R_(s)), and in even more particular cases, part-span connector(s) 218 are located at approximately 57 percent of the radial span (R_(s)). In some cases, each part-span connector 218 is sized to complement a corresponding part-span connector on an adjacent turbine bucket 200, as illustrated in the schematic view of two adjacent buckets 200 in FIG. 4. According to various embodiments, each part-span connector 218 has an axial width (measured along axis A) of approximately 40 percent to approximately 60 percent of an axial width of airfoil 202, as measured at the radial location of part-span connector 218. In some cases, each part-span connector is located between approximately 25 percent and approximately 75 percent of an axial chord length of airfoil 202.

In various embodiments, the part-span connector 218 allows for improved aerodynamic tuning when compared with conventional buckets, allowing for fewer tuning-related failures, and improving the efficiency of fluid flow within a turbine utilizing such a bucket 200.

With reference to FIG. 1, in various embodiments, the bucket 200 can include a fourth stage bucket (L1). In particular embodiments, the improved flow profile across the airfoil 200 and base 212 interface allows that fourth stage bucket (L1) to withstand the high-heat gas entering the turbine 10 at that fourth stage. In various embodiments, the turbine 10 can include a set of buckets 200 in only the fourth stage (L1) of the turbine 10, or in only the third stage (L2) and the fourth stage (L1) of the turbine 10.

FIG. 5 shows a schematic depiction of a set of buckets 200, with illustration of the part-span connector 218 removed in order to demonstrate additional features of the bucket 200. It is understood that buckets 200 would each include a pair of part-span connectors 218 if shown in complete detail. With reference to FIG. 5 (and continuing reference to FIGS. 2-4), a plurality of points 270-278 along span S, including root 215 and tip 217, can correspond to Z coordinate values of chord lines, and a cross section of airfoil 202 at each point can be described by a respective set of X and Y coordinates. For example, 100 points can be listed for each cross section 270-278, though it should be apparent that more or fewer points can be used for each cross section, and more or fewer cross sections can be used, as may be desired and/or appropriate. The X, Y, and Z coordinate values in TABLE I have been expressed in normalized or non-dimensionalized form in values of from 0 to 1, but it should be apparent that any or all of the coordinate values could instead be expressed in distance units so long as the proportions are maintained. To convert an X, Y or Z value of TABLE I to a respective X, Y or Z coordinate value in units of distance, such as inches or meters, the non-dimensional X, Y or Z value given in TABLE I can be multiplied by an airfoil height of airfoil 202 in such units of distance. By connecting the X and Y values with smooth continuing arcs, each profile cross section at each distance Z can be fixed, and the airfoil profiles of the various surface locations between the distances Z can be determined by smoothly connecting adjacent profile sections to one another, thus forming the airfoil profile.

The values in TABLE I are generated and shown to four decimal places for determining the profile of a nominal airfoil 202 at ambient, non-operating, or non-hot conditions, and do not take any coatings or fillets into account, though embodiments could account for other conditions, coatings, and/or fillets. To allow for typical manufacturing tolerances and/or coating thicknesses, ± values can be added to the values listed in TABLE I, particularly to the X and Y values therein. For example, a tolerance of about 10-20 percent of a thickness of the trailing edge in a direction normal to any surface location along the airfoil profile can define an airfoil profile envelope for a bucket airfoil design at cold or room temperature. In other words, a distance of about 10-20 percent of a thickness of the trailing edge in a direction normal to any surface location along the airfoil profile can define a range of variation between measured points on an actual airfoil surface and ideal positions of those points, particularly at a cold or room temperature, as embodied by the invention. The bucket airfoil design, as embodied by the invention, is robust to this range of variation without impairment of mechanical and aerodynamic functions. Likewise, the profile and/or design can be scaled up or down, such as geometrically, without impairment of operation, and such scaling can be facilitated by use of normalized coordinate values, i.e. multiplying the normalized values by a scaling factor, or a larger or smaller number of distance units than might have originally been used. For example, the values in TABLE I, particularly the X and Y values, could be multiplied by a scaling factor of 2, 0.5, or any other desired scaling factor. In various embodiments, the X, Y, and Z distances are scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil. Alternatively, the values could be multiplied by a larger or smaller desired span. As referenced herein, the origin of the X, Y, Z coordinate system is the root of the leading edge (junction 232) of the airfoil 202.

TABLE 1 Non-Dimensionalized (X Y Z/Span Height) N Location X Y Z 1 Suction-Side −0.0750 0.4078 0 2 Suction-Side 0.0000 0.0000 0 3 Suction-Side 0.0922 0.8028 0 4 Suction-Side 0.3356 1.1576 0 5 Suction-Side 0.6131 1.4868 0 6 Suction-Side 0.9114 1.7968 0 7 Suction-Side 1.2250 2.0919 0 8 Suction-Side 1.5486 2.3758 0 9 Suction-Side 1.8802 2.6501 0 10 Suction-Side 2.2194 2.9151 0 11 Suction-Side 2.5655 3.1717 0 12 Suction-Side 2.9167 3.4203 0 13 Suction-Side 3.2732 3.6617 0 14 Suction-Side 3.6341 3.8967 0 15 Suction-Side 3.9986 4.1257 0 16 Suction-Side 4.3671 4.3486 0 17 Suction-Side 4.7392 4.5651 0 18 Suction-Side 5.1145 4.7757 0 19 Suction-Side 5.4938 4.9798 0 20 Suction-Side 5.8759 5.1778 0 21 Suction-Side 6.2613 5.3699 0 22 Suction-Side 6.6494 5.5560 0 23 Suction-Side 7.0408 5.7360 0 24 Suction-Side 7.4345 5.9100 0 25 Suction-Side 7.8307 6.0780 0 26 Suction-Side 8.2297 6.2404 0 27 Suction-Side 8.6307 6.3968 0 28 Suction-Side 9.0340 6.5472 0 29 Suction-Side 9.4398 6.6915 0 30 Suction-Side 9.8476 6.8295 0 31 Suction-Side 10.2574 6.9614 0 32 Suction-Side 10.6692 7.0873 0 33 Suction-Side 11.0826 7.2064 0 34 Suction-Side 11.4981 7.3195 0 35 Suction-Side 11.9155 7.4261 0 36 Suction-Side 12.3341 7.5264 0 37 Suction-Side 12.7543 7.6198 0 38 Suction-Side 13.1757 7.7072 0 39 Suction-Side 13.5988 7.7878 0 40 Suction-Side 14.0230 7.8620 0 41 Suction-Side 14.4481 7.9293 0 42 Suction-Side 14.8743 7.9903 0 43 Suction-Side 15.3013 8.0444 0 44 Suction-Side 15.7292 8.0913 0 45 Suction-Side 16.1578 8.1314 0 46 Suction-Side 16.5873 8.1647 0 47 Suction-Side 17.0171 8.1912 0 48 Suction-Side 17.4470 8.2100 0 49 Suction-Side 17.8776 8.2221 0 50 Suction-Side 18.3079 8.2269 0 51 Suction-Side 18.7385 8.2249 0 52 Suction-Side 19.1688 8.2152 0 53 Suction-Side 19.5990 8.1980 0 54 Suction-Side 20.0289 8.1735 0 55 Suction-Side 20.4583 8.1415 0 56 Suction-Side 20.8870 8.1014 0 57 Suction-Side 21.3148 8.0537 0 58 Suction-Side 21.7419 7.9979 0 59 Suction-Side 22.1673 7.9342 0 60 Suction-Side 22.5919 7.8624 0 61 Suction-Side 23.0150 7.7826 0 62 Suction-Side 23.4364 7.6944 0 63 Suction-Side 23.8558 7.5977 0 64 Suction-Side 24.2732 7.4923 0 65 Suction-Side 24.6886 7.3788 0 66 Suction-Side 25.1012 7.2561 0 67 Suction-Side 25.5114 7.1254 0 68 Suction-Side 25.9188 6.9858 0 69 Suction-Side 26.3230 6.8379 0 70 Suction-Side 26.7244 6.6819 0 71 Suction-Side 27.1222 6.5171 0 72 Suction-Side 27.5163 6.3443 0 73 Suction-Side 27.9069 6.1626 0 74 Suction-Side 28.2934 5.9730 0 75 Suction-Side 28.6756 5.7749 0 76 Suction-Side 29.0533 5.5684 0 77 Suction-Side 29.4266 5.3539 0 78 Suction-Side 29.7955 5.1317 0 79 Suction-Side 30.1596 4.9024 0 80 Suction-Side 30.5193 4.6658 0 81 Suction-Side 30.8745 4.4220 0 82 Suction-Side 31.2250 4.1722 0 83 Suction-Side 31.5710 3.9160 0 84 Suction-Side 31.9123 3.6537 0 85 Suction-Side 32.2491 3.3855 0 86 Suction-Side 32.5815 3.1120 0 87 Suction-Side 32.9095 2.8329 0 88 Suction-Side 33.2327 2.5486 0 89 Suction-Side 33.5523 2.2603 0 90 Suction-Side 33.8682 1.9676 0 91 Suction-Side 34.1802 1.6709 0 92 Suction-Side 34.4882 1.3701 0 93 Suction-Side 34.7925 1.0654 0 94 Suction-Side 35.0924 0.7570 0 95 Suction-Side 35.3896 0.4451 0 96 Suction-Side 35.6831 0.1303 0 97 Suction-Side 35.9746 −0.1865 0 98 Suction-Side 36.2645 −0.5048 0 99 Suction-Side 36.5095 −1.2226 0 100 Suction-Side 36.5496 −0.8272 0 101 Pressure-Side 36.1550 −1.2799 0 102 Pressure-Side 35.8599 −1.0393 0 103 Pressure-Side 35.5648 −0.7971 0 104 Pressure-Side 35.2652 −0.5606 0 105 Pressure-Side 34.9601 −0.3312 0 106 Pressure-Side 34.6489 −0.1099 0 107 Pressure-Side 34.3322 0.1031 0 108 Pressure-Side 34.0106 0.3088 0 109 Pressure-Side 33.6850 0.5076 0 110 Pressure-Side 33.3558 0.7009 0 111 Pressure-Side 33.0238 0.8894 0 112 Pressure-Side 32.6898 1.0742 0 113 Pressure-Side 32.3541 1.2555 0 114 Pressure-Side 32.0157 1.4323 0 115 Pressure-Side 31.6745 1.6039 0 116 Pressure-Side 31.3312 1.7699 0 117 Pressure-Side 30.9852 1.9311 0 118 Pressure-Side 30.6364 2.0871 0 119 Pressure-Side 30.2859 2.2375 0 120 Pressure-Side 29.9330 2.3830 0 121 Pressure-Side 29.5778 2.5230 0 122 Pressure-Side 29.2209 2.6581 0 123 Pressure-Side 28.8616 2.7876 0 124 Pressure-Side 28.5011 2.9123 0 125 Pressure-Side 28.1383 3.0314 0 126 Pressure-Side 27.7742 3.1457 0 127 Pressure-Side 27.4085 3.2547 0 128 Pressure-Side 27.0412 3.3586 0 129 Pressure-Side 26.6723 3.4572 0 130 Pressure-Side 26.3022 3.5511 0 131 Pressure-Side 25.9309 3.6397 0 132 Pressure-Side 25.5588 3.7235 0 133 Pressure-Side 25.1851 3.8025 0 134 Pressure-Side 24.8105 3.8767 0 135 Pressure-Side 24.4352 3.9456 0 136 Pressure-Side 24.0591 4.0106 0 137 Pressure-Side 23.6822 4.0703 0 138 Pressure-Side 23.3045 4.1257 0 139 Pressure-Side 22.9263 4.1762 0 140 Pressure-Side 22.5474 4.2223 0 141 Pressure-Side 22.1677 4.2640 0 142 Pressure-Side 21.7880 4.3013 0 143 Pressure-Side 21.4078 4.3342 0 144 Pressure-Side 21.0269 4.3626 0 145 Pressure-Side 20.6460 4.3871 0 146 Pressure-Side 20.2650 4.4068 0 147 Pressure-Side 19.8837 4.4228 0 148 Pressure-Side 19.5020 4.4340 0 149 Pressure-Side 19.1203 4.4416 0 150 Pressure-Side 18.7385 4.4452 0 151 Pressure-Side 18.3572 4.4444 0 152 Pressure-Side 17.9755 4.4400 0 153 Pressure-Side 17.5937 4.4316 0 154 Pressure-Side 17.2124 4.4196 0 155 Pressure-Side 16.8307 4.4031 0 156 Pressure-Side 16.4497 4.3831 0 157 Pressure-Side 16.0688 4.3590 0 158 Pressure-Side 15.6879 4.3310 0 159 Pressure-Side 15.3078 4.2993 0 160 Pressure-Side 14.9276 4.2632 0 161 Pressure-Side 14.5479 4.2239 0 162 Pressure-Side 14.1686 4.1802 0 163 Pressure-Side 13.7900 4.1329 0 164 Pressure-Side 13.4119 4.0820 0 165 Pressure-Side 13.0342 4.0266 0 166 Pressure-Side 12.6569 3.9677 0 167 Pressure-Side 12.2804 3.9047 0 168 Pressure-Side 11.9046 3.8382 0 169 Pressure-Side 11.5297 3.7672 0 170 Pressure-Side 11.1552 3.6926 0 171 Pressure-Side 10.7819 3.6136 0 172 Pressure-Side 10.4090 3.5310 0 173 Pressure-Side 10.0373 3.4444 0 174 Pressure-Side 9.6668 3.3534 0 175 Pressure-Side 9.2967 3.2588 0 176 Pressure-Side 8.9282 3.1597 0 177 Pressure-Side 8.5605 3.0571 0 178 Pressure-Side 8.1944 2.9496 0 179 Pressure-Side 7.8291 2.8385 0 180 Pressure-Side 7.4650 2.7234 0 181 Pressure-Side 7.1025 2.6048 0 182 Pressure-Side 6.7408 2.4825 0 183 Pressure-Side 6.3808 2.3561 0 184 Pressure-Side 6.0215 2.2266 0 185 Pressure-Side 5.6638 2.0935 0 186 Pressure-Side 5.3073 1.9576 0 187 Pressure-Side 4.9521 1.8180 0 188 Pressure-Side 4.5980 1.6753 0 189 Pressure-Side 4.2452 1.5297 0 190 Pressure-Side 3.8935 1.3810 0 191 Pressure-Side 3.5426 1.2306 0 192 Pressure-Side 3.1926 1.0782 0 193 Pressure-Side 2.8429 0.9251 0 194 Pressure-Side 2.4937 0.7707 0 195 Pressure-Side 2.1448 0.6167 0 196 Pressure-Side 1.7952 0.4631 0 197 Pressure-Side 1.4439 0.3136 0 198 Pressure-Side 1.0899 0.1708 0 199 Pressure-Side 0.7310 0.0409 0 200 Pressure-Side 0.3621 −0.0553 0 1 Suction-Side 2.3313 2.2567 10 2 Suction-Side 2.3654 1.8806 10 3 Suction-Side 2.5073 2.6044 10 4 Suction-Side 2.7491 2.9115 10 5 Suction-Side 3.0202 3.1930 10 6 Suction-Side 3.3093 3.4564 10 7 Suction-Side 3.6108 3.7054 10 8 Suction-Side 3.9212 3.9432 10 9 Suction-Side 4.2383 4.1718 10 10 Suction-Side 4.5623 4.3907 10 11 Suction-Side 4.8919 4.6012 10 12 Suction-Side 5.2264 4.8041 10 13 Suction-Side 5.5648 4.9994 10 14 Suction-Side 5.9076 5.1879 10 15 Suction-Side 6.2533 5.3703 10 16 Suction-Side 6.6029 5.5459 10 17 Suction-Side 6.9554 5.7151 10 18 Suction-Side 7.3110 5.8779 10 19 Suction-Side 7.6691 6.0343 10 20 Suction-Side 8.0304 6.1847 10 21 Suction-Side 8.3937 6.3286 10 22 Suction-Side 8.7594 6.4666 10 23 Suction-Side 9.1275 6.5989 10 24 Suction-Side 9.4976 6.7248 10 25 Suction-Side 9.8697 6.8455 10 26 Suction-Side 10.2434 6.9602 10 27 Suction-Side 10.6191 7.0692 10 28 Suction-Side 10.9960 7.1727 10 29 Suction-Side 11.3746 7.2705 10 30 Suction-Side 11.7547 7.3628 10 31 Suction-Side 12.1360 7.4490 10 32 Suction-Side 12.5185 7.5296 10 33 Suction-Side 12.9027 7.6046 10 34 Suction-Side 13.2872 7.6735 10 35 Suction-Side 13.6734 7.7369 10 36 Suction-Side 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8.1952 80 172 Pressure-Side 17.1069 8.3223 80 173 Pressure-Side 16.9899 8.4490 80 174 Pressure-Side 16.8720 8.5749 80 175 Pressure-Side 16.7537 8.7004 80 176 Pressure-Side 16.6346 8.8251 80 177 Pressure-Side 16.5147 8.9490 80 178 Pressure-Side 16.3940 9.0721 80 179 Pressure-Side 16.2721 9.1944 80 180 Pressure-Side 16.1494 9.3155 80 181 Pressure-Side 16.0255 9.4354 80 182 Pressure-Side 15.9004 9.5541 80 183 Pressure-Side 15.7745 9.6716 80 184 Pressure-Side 15.6470 9.7879 80 185 Pressure-Side 15.5179 9.9022 80 186 Pressure-Side 15.3879 10.0152 80 187 Pressure-Side 15.2560 10.1267 80 188 Pressure-Side 15.1229 10.2362 80 189 Pressure-Side 14.9882 10.3440 80 190 Pressure-Side 14.8518 10.4495 80 191 Pressure-Side 14.7139 10.5534 80 192 Pressure-Side 14.5744 10.6544 80 193 Pressure-Side 14.4332 10.7534 80 194 Pressure-Side 14.2905 10.8505 80 195 Pressure-Side 14.1465 10.9447 80 196 Pressure-Side 14.0006 11.0373 80 197 Pressure-Side 13.8542 11.1280 80 198 Pressure-Side 13.7074 11.2186 80 199 Pressure-Side 13.5615 11.3108 80 200 Pressure-Side 13.4236 11.4138 80 1 Suction-Side 14.3542 12.3449 90 2 Suction-Side 14.4657 12.4760 90 3 Suction-Side 14.6157 12.5610 90 4 Suction-Side 14.7833 12.6015 90 5 Suction-Side 14.9561 12.6096 90 6 Suction-Side 15.1285 12.5943 90 7 Suction-Side 15.2981 12.5610 90 8 Suction-Side 15.4649 12.5145 90 9 Suction-Side 15.6281 12.4572 90 10 Suction-Side 15.7877 12.3902 90 11 Suction-Side 15.9433 12.3148 90 12 Suction-Side 16.0953 12.2322 90 13 Suction-Side 16.2436 12.1432 90 14 Suction-Side 16.3888 12.0486 90 15 Suction-Side 16.5303 11.9488 90 16 Suction-Side 16.6687 11.8449 90 17 Suction-Side 16.8034 11.7366 90 18 Suction-Side 16.9353 11.6248 90 19 Suction-Side 17.0644 11.5093 90 20 Suction-Side 17.1903 11.3906 90 21 Suction-Side 17.3134 11.2691 90 22 Suction-Side 17.4345 11.1452 90 23 Suction-Side 17.5528 11.0189 90 24 Suction-Side 17.6695 10.8910 90 25 Suction-Side 17.7842 10.7615 90 26 Suction-Side 17.8973 10.6303 90 27 Suction-Side 18.0087 10.4980 90 28 Suction-Side 18.1190 10.3649 90 29 Suction-Side 18.2281 10.2302 90 30 Suction-Side 18.3355 10.0950 90 31 Suction-Side 18.4422 9.9583 90 32 Suction-Side 18.5477 9.8212 90 33 Suction-Side 18.6523 9.6832 90 34 Suction-Side 18.7558 9.5449 90 35 Suction-Side 18.8588 9.4058 90 36 Suction-Side 18.9611 9.2658 90 37 Suction-Side 19.0625 9.1259 90 38 Suction-Side 19.1636 8.9855 90 39 Suction-Side 19.2642 8.8444 90 40 Suction-Side 19.3644 8.7036 90 41 Suction-Side 19.4643 8.5621 90 42 Suction-Side 19.5641 8.4205 90 43 Suction-Side 19.6632 8.2790 90 44 Suction-Side 19.7622 8.1371 90 45 Suction-Side 19.8609 7.9947 90 46 Suction-Side 19.9595 7.8524 90 47 Suction-Side 20.0577 7.7100 90 48 Suction-Side 20.1560 7.5677 90 49 Suction-Side 20.2538 7.4249 90 50 Suction-Side 20.3521 7.2822 90 51 Suction-Side 20.4499 7.1394 90 52 Suction-Side 20.5477 6.9967 90 53 Suction-Side 20.6456 6.8539 90 54 Suction-Side 20.7434 6.7112 90 55 Suction-Side 20.8413 6.5684 90 56 Suction-Side 20.9391 6.4257 90 57 Suction-Side 21.0369 6.2829 90 58 Suction-Side 21.1348 6.1402 90 59 Suction-Side 21.2326 5.9974 90 60 Suction-Side 21.3304 5.8547 90 61 Suction-Side 21.4283 5.7119 90 62 Suction-Side 21.5261 5.5692 90 63 Suction-Side 21.6240 5.4264 90 64 Suction-Side 21.7218 5.2841 90 65 Suction-Side 21.8200 5.1413 90 66 Suction-Side 21.9179 4.9986 90 67 Suction-Side 22.0161 4.8562 90 68 Suction-Side 22.1144 4.7135 90 69 Suction-Side 22.2126 4.5712 90 70 Suction-Side 22.3108 4.4288 90 71 Suction-Side 22.4091 4.2861 90 72 Suction-Side 22.5073 4.1437 90 73 Suction-Side 22.6060 4.0018 90 74 Suction-Side 22.7046 3.8594 90 75 Suction-Side 22.8032 3.7171 90 76 Suction-Side 22.9019 3.5751 90 77 Suction-Side 23.0009 3.4328 90 78 Suction-Side 23.0996 3.2908 90 79 Suction-Side 23.1982 3.1489 90 80 Suction-Side 23.2972 3.0065 90 81 Suction-Side 23.3959 2.8646 90 82 Suction-Side 23.4945 2.7222 90 83 Suction-Side 23.5936 2.5803 90 84 Suction-Side 23.6922 2.4383 90 85 Suction-Side 23.7908 2.2960 90 86 Suction-Side 23.8895 2.1541 90 87 Suction-Side 23.9885 2.0117 90 88 Suction-Side 24.0872 1.8698 90 89 Suction-Side 24.1858 1.7274 90 90 Suction-Side 24.2845 1.5855 90 91 Suction-Side 24.3831 1.4431 90 92 Suction-Side 24.4817 1.3012 90 93 Suction-Side 24.5808 1.1588 90 94 Suction-Side 24.6794 1.0169 90 95 Suction-Side 24.7781 0.8745 90 96 Suction-Side 24.8767 0.7322 90 97 Suction-Side 24.9753 0.5902 90 98 Suction-Side 25.0391 0.1375 90 99 Suction-Side 25.0744 0.4483 90 100 Suction-Side 25.1197 0.2855 90 101 Pressure-Side 24.8863 0.0974 90 102 Pressure-Side 24.7468 0.1720 90 103 Pressure-Side 24.6437 0.2975 90 104 Pressure-Side 24.5415 0.4230 90 105 Pressure-Side 24.4388 0.5485 90 106 Pressure-Side 24.3358 0.6740 90 107 Pressure-Side 24.2331 0.7996 90 108 Pressure-Side 24.1301 0.9247 90 109 Pressure-Side 24.0270 1.0498 90 110 Pressure-Side 23.9236 1.1749 90 111 Pressure-Side 23.8205 1.3000 90 112 Pressure-Side 23.7167 1.4247 90 113 Pressure-Side 23.6132 1.5494 90 114 Pressure-Side 23.5094 1.6737 90 115 Pressure-Side 23.4051 1.7984 90 116 Pressure-Side 23.3009 1.9223 90 117 Pressure-Side 23.1966 2.0466 90 118 Pressure-Side 23.0919 2.1705 90 119 Pressure-Side 22.9873 2.2944 90 120 Pressure-Side 22.8826 2.4183 90 121 Pressure-Side 22.7776 2.5418 90 122 Pressure-Side 22.6729 2.6657 90 123 Pressure-Side 22.5679 2.7892 90 124 Pressure-Side 22.4628 2.9127 90 125 Pressure-Side 22.3582 3.0362 90 126 Pressure-Side 22.2531 3.1601 90 127 Pressure-Side 22.1480 3.2836 90 128 Pressure-Side 22.0430 3.4071 90 129 Pressure-Side 21.9379 3.5306 90 130 Pressure-Side 21.8333 3.6545 90 131 Pressure-Side 21.7282 3.7780 90 132 Pressure-Side 21.6236 3.9019 90 133 Pressure-Side 21.5189 4.0258 90 134 Pressure-Side 21.4143 4.1493 90 135 Pressure-Side 21.3096 4.2732 90 136 Pressure-Side 21.2049 4.3975 90 137 Pressure-Side 21.1007 4.5214 90 138 Pressure-Side 20.9964 4.6457 90 139 Pressure-Side 20.8922 4.7700 90 140 Pressure-Side 20.7883 4.8943 90 141 Pressure-Side 20.6845 5.0190 90 142 Pressure-Side 20.5806 5.1438 90 143 Pressure-Side 20.4772 5.2685 90 144 Pressure-Side 20.3737 5.3932 90 145 Pressure-Side 20.2707 5.5183 90 146 Pressure-Side 20.1676 5.6438 90 147 Pressure-Side 20.0646 5.7693 90 148 Pressure-Side 19.9623 5.8948 90 149 Pressure-Side 19.8597 6.0207 90 150 Pressure-Side 19.7578 6.1466 90 151 Pressure-Side 19.6560 6.2725 90 152 Pressure-Side 19.5541 6.3992 90 153 Pressure-Side 19.4531 6.5255 90 154 Pressure-Side 19.3516 6.6522 90 155 Pressure-Side 19.2506 6.7789 90 156 Pressure-Side 19.1499 6.9061 90 157 Pressure-Side 19.0489 7.0332 90 158 Pressure-Side 18.9482 7.1603 90 159 Pressure-Side 18.8476 7.2874 90 160 Pressure-Side 18.7469 7.4145 90 161 Pressure-Side 18.6463 7.5416 90 162 Pressure-Side 18.5457 7.6687 90 163 Pressure-Side 18.4446 7.7958 90 164 Pressure-Side 18.3440 7.9225 90 165 Pressure-Side 18.2429 8.0496 90 166 Pressure-Side 18.1419 8.1764 90 167 Pressure-Side 18.0404 8.3031 90 168 Pressure-Side 17.9390 8.4294 90 169 Pressure-Side 17.8371 8.5557 90 170 Pressure-Side 17.7349 8.6816 90 171 Pressure-Side 17.6326 8.8075 90 172 Pressure-Side 17.5300 8.9330 90 173 Pressure-Side 17.4269 9.0581 90 174 Pressure-Side 17.3235 9.1832 90 175 Pressure-Side 17.2200 9.3075 90 176 Pressure-Side 17.1158 9.4318 90 177 Pressure-Side 17.0107 9.5557 90 178 Pressure-Side 16.9056 9.6788 90 179 Pressure-Side 16.7994 9.8015 90 180 Pressure-Side 16.6927 9.9238 90 181 Pressure-Side 16.5853 10.0453 90 182 Pressure-Side 16.4770 10.1660 90 183 Pressure-Side 16.3679 10.2859 90 184 Pressure-Side 16.2581 10.4050 90 185 Pressure-Side 16.1470 10.5233 90 186 Pressure-Side 16.0347 10.6404 90 187 Pressure-Side 15.9216 10.7566 90 188 Pressure-Side 15.8078 10.8717 90 189 Pressure-Side 15.6923 10.9856 90 190 Pressure-Side 15.5756 11.0983 90 191 Pressure-Side 15.4577 11.2098 90 192 Pressure-Side 15.3390 11.3200 90 193 Pressure-Side 15.2187 11.4291 90 194 Pressure-Side 15.0976 11.5370 90 195 Pressure-Side 14.9757 11.6436 90 196 Pressure-Side 14.8526 11.7495 90 197 Pressure-Side 14.7295 11.8549 90 198 Pressure-Side 14.6076 11.9616 90 199 Pressure-Side 14.4886 12.0719 90 200 Pressure-Side 14.3815 12.1934 90 1 Suction-Side 14.9669 13.0879 100 2 Suction-Side 15.0940 13.1918 100 3 Suction-Side 15.2516 13.2415 100 4 Suction-Side 15.4172 13.2519 100 5 Suction-Side 15.5820 13.2351 100 6 Suction-Side 15.7440 13.1982 100 7 Suction-Side 15.9012 13.1457 100 8 Suction-Side 16.0540 13.0811 100 9 Suction-Side 16.2023 13.0065 100 10 Suction-Side 16.3463 12.9235 100 11 Suction-Side 16.4854 12.8333 100 12 Suction-Side 16.6206 12.7371 100 13 Suction-Side 16.7521 12.6356 100 14 Suction-Side 16.8800 12.5302 100 15 Suction-Side 17.0051 12.4211 100 16 Suction-Side 17.1274 12.3088 100 17 Suction-Side 17.2469 12.1934 100 18 Suction-Side 17.3636 12.0755 100 19 Suction-Side 17.4782 11.9552 100 20 Suction-Side 17.5901 11.8329 100 21 Suction-Side 17.7000 11.7086 100 22 Suction-Side 17.8083 11.5827 100 23 Suction-Side 17.9149 11.4552 100 24 Suction-Side 18.0196 11.3268 100 25 Suction-Side 18.1234 11.1973 100 26 Suction-Side 18.2261 11.0666 100 27 Suction-Side 18.3279 10.9355 100 28 Suction-Side 18.4286 10.8040 100 29 Suction-Side 18.5288 10.6712 100 30 Suction-Side 18.6279 10.5381 100 31 Suction-Side 18.7261 10.4046 100 32 Suction-Side 18.8239 10.2703 100 33 Suction-Side 18.9210 10.1355 100 34 Suction-Side 19.0176 10.0008 100 35 Suction-Side 19.1138 9.8653 100 36 Suction-Side 19.2093 9.7297 100 37 Suction-Side 19.3047 9.5938 100 38 Suction-Side 19.4001 9.4579 100 39 Suction-Side 19.4952 9.3219 100 40 Suction-Side 19.5898 9.1856 100 41 Suction-Side 19.6844 9.0493 100 42 Suction-Side 19.7791 8.9129 100 43 Suction-Side 19.8733 8.7762 100 44 Suction-Side 19.9675 8.6395 100 45 Suction-Side 20.0613 8.5027 100 46 Suction-Side 20.1556 8.3660 100 47 Suction-Side 20.2494 8.2293 100 48 Suction-Side 20.3432 8.0921 100 49 Suction-Side 20.4371 7.9554 100 50 Suction-Side 20.5309 7.8183 100 51 Suction-Side 20.6247 7.6815 100 52 Suction-Side 20.7190 7.5448 100 53 Suction-Side 20.8128 7.4077 100 54 Suction-Side 20.9066 7.2709 100 55 Suction-Side 21.0004 7.1342 100 56 Suction-Side 21.0943 6.9971 100 57 Suction-Side 21.1885 6.8603 100 58 Suction-Side 21.2823 6.7236 100 59 Suction-Side 21.3762 6.5869 100 60 Suction-Side 21.4704 6.4501 100 61 Suction-Side 21.5646 6.3134 100 62 Suction-Side 21.6584 6.1767 100 63 Suction-Side 21.7527 6.0399 100 64 Suction-Side 21.8469 5.9032 100 65 Suction-Side 21.9411 5.7665 100 66 Suction-Side 22.0354 5.6297 100 67 Suction-Side 22.1296 5.4934 100 68 Suction-Side 22.2242 5.3567 100 69 Suction-Side 22.3185 5.2203 100 70 Suction-Side 22.4131 5.0840 100 71 Suction-Side 22.5077 4.9473 100 72 Suction-Side 22.6023 4.8109 100 73 Suction-Side 22.6970 4.6746 100 74 Suction-Side 22.7916 4.5383 100 75 Suction-Side 22.8866 4.4023 100 76 Suction-Side 22.9813 4.2660 100 77 Suction-Side 23.0763 4.1297 100 78 Suction-Side 23.1713 3.9937 100 79 Suction-Side 23.2660 3.8574 100 80 Suction-Side 23.3610 3.7215 100 81 Suction-Side 23.4560 3.5851 100 82 Suction-Side 23.5511 3.4492 100 83 Suction-Side 23.6461 3.3129 100 84 Suction-Side 23.7411 3.1770 100 85 Suction-Side 23.8362 3.0410 100 86 Suction-Side 23.9312 2.9047 100 87 Suction-Side 24.0262 2.7688 100 88 Suction-Side 24.1217 2.6328 100 89 Suction-Side 24.2167 2.4969 100 90 Suction-Side 24.3117 2.3610 100 91 Suction-Side 24.4068 2.2246 100 92 Suction-Side 24.5022 2.0887 100 93 Suction-Side 24.5972 1.9528 100 94 Suction-Side 24.6922 1.8168 100 95 Suction-Side 24.7877 1.6809 100 96 Suction-Side 24.8827 1.5450 100 97 Suction-Side 24.9781 1.4090 100 98 Suction-Side 25.0219 0.9704 100 99 Suction-Side 25.0724 1.2727 100 100 Suction-Side 25.1008 1.1123 100 101 Pressure-Side 24.8755 0.9227 100 102 Pressure-Side 24.7331 0.9812 100 103 Pressure-Side 24.6301 1.0999 100 104 Pressure-Side 24.5286 1.2202 100 105 Pressure-Side 24.4268 1.3405 100 106 Pressure-Side 24.3254 1.4604 100 107 Pressure-Side 24.2239 1.5807 100 108 Pressure-Side 24.1221 1.7010 100 109 Pressure-Side 24.0206 1.8212 100 110 Pressure-Side 23.9188 1.9411 100 111 Pressure-Side 23.8173 2.0614 100 112 Pressure-Side 23.7155 2.1817 100 113 Pressure-Side 23.6140 2.3020 100 114 Pressure-Side 23.5126 2.4223 100 115 Pressure-Side 23.4107 2.5422 100 116 Pressure-Side 23.3093 2.6625 100 117 Pressure-Side 23.2078 2.7832 100 118 Pressure-Side 23.1064 2.9035 100 119 Pressure-Side 23.0053 3.0238 100 120 Pressure-Side 22.9039 3.1445 100 121 Pressure-Side 22.8028 3.2652 100 122 Pressure-Side 22.7018 3.3859 100 123 Pressure-Side 22.6007 3.5066 100 124 Pressure-Side 22.5001 3.6273 100 125 Pressure-Side 22.3995 3.7483 100 126 Pressure-Side 22.2988 3.8694 100 127 Pressure-Side 22.1982 3.9905 100 128 Pressure-Side 22.0979 4.1116 100 129 Pressure-Side 21.9977 4.2331 100 130 Pressure-Side 21.8974 4.3546 100 131 Pressure-Side 21.7976 4.4761 100 132 Pressure-Side 21.6977 4.5976 100 133 Pressure-Side 21.5979 4.7195 100 134 Pressure-Side 21.4981 4.8410 100 135 Pressure-Side 21.3986 4.9629 100 136 Pressure-Side 21.2992 5.0852 100 137 Pressure-Side 21.1997 5.2071 100 138 Pressure-Side 21.1007 5.3294 100 139 Pressure-Side 21.0016 5.4517 100 140 Pressure-Side 20.9030 5.5744 100 141 Pressure-Side 20.8040 5.6971 100 142 Pressure-Side 20.7057 5.8198 100 143 Pressure-Side 20.6071 5.9425 100 144 Pressure-Side 20.5088 6.0656 100 145 Pressure-Side 20.4106 6.1887 100 146 Pressure-Side 20.3128 6.3118 100 147 Pressure-Side 20.2149 6.4349 100 148 Pressure-Side 20.1175 6.5584 100 149 Pressure-Side 20.0200 6.6823 100 150 Pressure-Side 19.9226 6.8058 100 151 Pressure-Side 19.8256 6.9297 100 152 Pressure-Side 19.7289 7.0540 100 153 Pressure-Side 19.6323 7.1779 100 154 Pressure-Side 19.5357 7.3026 100 155 Pressure-Side 19.4394 7.4269 100 156 Pressure-Side 19.3432 7.5516 100 157 Pressure-Side 19.2474 7.6763 100 158 Pressure-Side 19.1515 7.8010 100 159 Pressure-Side 19.0553 7.9257 100 160 Pressure-Side 18.9595 8.0508 100 161 Pressure-Side 18.8636 8.1755 100 162 Pressure-Side 18.7678 8.3003 100 163 Pressure-Side 18.6720 8.4254 100 164 Pressure-Side 18.5761 8.5501 100 165 Pressure-Side 18.4803 8.6748 100 166 Pressure-Side 18.3841 8.7995 100 167 Pressure-Side 18.2878 8.9242 100 168 Pressure-Side 18.1916 9.0485 100 169 Pressure-Side 18.0950 9.1728 100 170 Pressure-Side 17.9983 9.2971 100 171 Pressure-Side 17.9013 9.4210 100 172 Pressure-Side 17.8042 9.5449 100 173 Pressure-Side 17.7068 9.6684 100 174 Pressure-Side 17.6094 9.7919 100 175 Pressure-Side 17.5111 9.9150 100 176 Pressure-Side 17.4129 10.0381 100 177 Pressure-Side 17.3138 10.1604 100 178 Pressure-Side 17.2148 10.2827 100 179 Pressure-Side 17.1150 10.4042 100 180 Pressure-Side 17.0147 10.5257 100 181 Pressure-Side 16.9137 10.6464 100 182 Pressure-Side 16.8122 10.7667 100 183 Pressure-Side 16.7104 10.8866 100 184 Pressure-Side 16.6077 11.0061 100 185 Pressure-Side 16.5043 11.1247 100 186 Pressure-Side 16.4004 11.2430 100 187 Pressure-Side 16.2958 11.3605 100 188 Pressure-Side 16.1903 11.4776 100 189 Pressure-Side 16.0840 11.5935 100 190 Pressure-Side 15.9774 11.7094 100 191 Pressure-Side 15.8703 11.8245 100 192 Pressure-Side 15.7625 11.9395 100 193 Pressure-Side 15.6550 12.0542 100 194 Pressure-Side 15.5467 12.1685 100 195 Pressure-Side 15.4393 12.2836 100 196 Pressure-Side 15.3326 12.3991 100 197 Pressure-Side 15.2280 12.5169 100 198 Pressure-Side 15.1253 12.6360 100 199 Pressure-Side 15.0319 12.7627 100 200 Pressure-Side 14.9597 12.9023 100

Turning to FIG. 6, a schematic view of portions of a multi-shaft combined cycle power plant 900 is shown. Combined cycle power plant 900 may include, for example, a gas turbine 980 operably connected to a generator 970. Generator 970 and gas turbine 980 may be mechanically coupled by a shaft 915, which may transfer energy between a drive shaft (not shown) of gas turbine 980 and generator 970. Also shown in FIG. 6 is a heat exchanger 986 operably connected to gas turbine 980 and a steam turbine 992. Heat exchanger 986 may be fluidly connected to both gas turbine 980 and a steam turbine 992 via conventional conduits (numbering omitted). Gas turbine 980 and/or steam turbine 992 may include one or more buckets 200 as shown and described with reference to FIG. 2 and/or other embodiments described herein. Heat exchanger 986 may be a conventional heat recovery steam generator (HRSG), such as those used in conventional combined cycle power systems. As is known in the art of power generation, HRSG 986 may use hot exhaust from gas turbine 980, combined with a water supply, to create steam which is fed to steam turbine 992. Steam turbine 992 may optionally be coupled to a second generator system 970 (via a second shaft 915). It is understood that generators 970 and shafts 915 may be of any size or type known in the art and may differ depending upon their application or the system to which they are connected. Common numbering of the generators and shafts is for clarity and does not necessarily suggest these generators or shafts are identical. In another embodiment, shown in FIG. 7, a single shaft combined cycle power plant 990 may include a single generator 970 coupled to both gas turbine 980 and steam turbine 992 via a single shaft 915. Steam turbine 992 and/or gas turbine 980 may include one or more buckets 200 shown and described with reference to FIG. 2 and/or other embodiments described herein.

The apparatus and devices of the present disclosure are not limited to any one particular engine, turbine, jet engine, generator, power generation system or other system, and may be used with other aircraft systems, power generation systems and/or systems (e.g., combined cycle, simple cycle, nuclear reactor, etc.). Additionally, the apparatus of the present invention may be used with other systems not described herein that may benefit from the increased reduced tip leakage and increased efficiency of the apparatus and devices described herein.

In various embodiments, components described as being “coupled” to one another can be joined along one or more interfaces. In some embodiments, these interfaces can include junctions between distinct components, and in other cases, these interfaces can include a solidly and/or integrally formed interconnection. That is, in some cases, components that are “coupled” to one another can be simultaneously formed to define a single continuous member. However, in other embodiments, these coupled components can be formed as separate members and be subsequently joined through known processes (e.g., fastening, ultrasonic welding, bonding).

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms “a”, “an” and “the” may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” “including,” and “having,” are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed.

When an element or layer is referred to as being “on”, “engaged to”, “connected to” or “coupled to” another element or layer, it may be directly on, engaged, connected or coupled to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to”, “directly connected to” or “directly coupled to” another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

Spatially relative terms, such as “inner,” “outer,” “beneath”, “below”, “lower”, “above”, “upper” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the example term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

The foregoing description of various aspects of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously, many modifications and variations are possible. Such modifications and variations that may be apparent to an individual in the art are included within the scope of the invention as defined by the accompanying claims.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

We claim:
 1. A turbine bucket comprising: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; a pair of part-span connectors extending from the airfoil at the suction side and the pressure side, respectively, wherein each of the pair of part-span connectors is located between approximately 40 percent and approximately 70 percent of a radial span measured from the base to a radial tip of the airfoil, wherein the pair of part-span connectors consists of a single part-span connector on each of the pressure side and the suction side of the airfoil; a base connected with a first end of the airfoil along the suction side, pressure side, trailing edge and the leading edge; and a shroud connected with a second end of the airfoil, the shroud located radially outboard of the airfoil and opposite the first end of the airfoil.
 2. The turbine bucket of claim 1, further comprising a fillet connecting a surface of the base to a surface of the airfoil.
 3. The turbine bucket of claim 1, wherein the turbine bucket includes a fourth stage bucket.
 4. The turbine bucket of claim 1, wherein the base directs flow of a working fluid across a passage trough proximate the suction side of the airfoil.
 5. The turbine bucket of claim 1, wherein the base is radially inboard of the airfoil.
 6. The turbine bucket of claim 1, wherein each part-span connector is sized to complement a single corresponding part-span connector on an adjacent turbine bucket, and wherein each of the pair of part-span connectors is located between approximately 56 percent and approximately 58 percent of the radial span of the airfoil.
 7. The turbine bucket of claim 6, wherein each of the pair of part-span connectors has an axial width of approximately 40 percent to approximately 60 percent of an axial width of the airfoil.
 8. The turbine bucket of claim 7, wherein each of the pair of part-span connectors is located between approximately 25 percent and approximately 75 percent of an axial chord length of the airfoil.
 9. The turbine bucket of claim 7, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Z coordinate values are non-dimensional values of from 0 to 1 convertible to Z distances by multiplying the values by an airfoil height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, the X, Y, and Z distances being scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.
 10. A turbine rotor section comprising: a set of buckets, the set of buckets including at least one bucket having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; a pair of part-span connectors extending from the airfoil at the suction side and the pressure side, respectively, wherein each of the pair of part-span connectors is located between approximately 40 percent and approximately 70 percent of a radial span measured from the base to a radial tip of the airfoil; and a base connected with a first end of the airfoil along the suction side, pressure side, trailing edge and the leading edge, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Z coordinate values are non-dimensional values of from 0 to 1 convertible to Z distances by multiplying the Z values by an airfoil height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, the X, Y, and Z distances being scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.
 11. The turbine rotor section of claim 10, further comprising a fillet connecting a surface of the base to a surface of the airfoil.
 12. The turbine rotor section of claim 10, wherein the turbine bucket includes a fourth stage bucket.
 13. The turbine rotor section of claim 10, wherein each part-span connector is sized to complement a corresponding part-span connector on an adjacent turbine bucket.
 14. The turbine rotor section of claim 10, wherein each of the pair of part-span connectors has an axial width of approximately 40 percent to approximately 60 percent of an axial width of the airfoil.
 15. The turbine rotor section of claim 14, wherein each of the pair of part-span connectors is located between approximately 25 percent and approximately 75 percent of an axial chord length of the airfoil.
 16. The turbine rotor section of claim 10, wherein the base directs flow of a working fluid across a passage trough proximate the suction side of the airfoil.
 17. A turbine bucket comprising: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and a base connected with a first end of the airfoil along the suction side, pressure side, trailing edge and the leading edge, wherein at least one of the suction side or the pressure side of the airfoil includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the coordinate values are non-dimensional values of from 0 to 1 convertible to Z distances by multiplying the Z values by an airfoil height expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along the airfoil, the profile sections at the Z distances being joined smoothly with one another to form the airfoil profile, the X, Y, and Z distances being scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil, wherein the Cartesian coordinate values have an origin at a root of the leading edge of the airfoil.
 18. The turbine bucket of claim 17, further comprising a pair of part-span connectors extending from the airfoil at the suction side and the pressure side, respectively, wherein each of the pair of part-span connectors is located between approximately 40 percent and approximately 70 percent of a radial span measured from the base to a radial tip of the airfoil.
 19. The turbine bucket of claim 18, wherein each part-span connector is sized to complement a corresponding part-span connector on an adjacent turbine bucket, wherein each of the pair of part-span connectors has an axial width of approximately 40 percent to approximately 60 percent of an axial width of the airfoil.
 20. The turbine bucket of claim 19, wherein each of the pair of part-span connectors is located between approximately 25 percent and approximately 75 percent of an axial chord length of the airfoil. 